Solve for y x=(y^2)/2

$x = \frac{y^{2}}{2}$

Step 1

Rewrite the equation as $\frac{y^{2}}{2} = x$ .

$\frac{y^{2}}{2} = x$

Step 2

Multiply both sides of the equation by $2$ .

$2 \frac{y^{2}}{2} = 2 x$

Step 3

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$2 \frac{y^{2}}{2} = 2 x$

Rewrite the expression.

$y^{2} = 2 x$

Step 4

Take the square root of both sides of the equation to eliminate the exponent on the left side.

$y = \pm \sqrt{2 x}$

Step 5

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the $\pm$ to find the first solution.

$y = \sqrt{2 x}$

Next, use the negative value of the $\pm$ to find the second solution.

$y = - \sqrt{2 x}$

The complete solution is the result of both the positive and negative portions of the solution.

$y = \sqrt{2 x}$

$y = - \sqrt{2 x}$

$y = \sqrt{2 x}$

$y = - \sqrt{2 x}$